Near-rings are very useful

Description

Near-rings are ?rings with just one distributive law and with possibly non-commutative addition?. Standard examples are collections M(G) of all mappings from a group (G,+) into itself, with point-wise addition and composition of mappings. If (G,+) is abelian and if one only takes endomorphisms (?linear maps?), one gets rings; so near-rings can be viewed as the ?non-linear generalizations of rings?. In this talk, I want to present an especially useful class of near-rings N, the planar ones. The are characterized by the property that all equations xa = xb + c have a unique solution x, unless xa = xb holds for all a,b ∈ N. If N ∗ = N \ {0}and one takes the collection B of all subsets of N of the form aN ∗ + b (with a not = 0) and their translates, one gets balanced incomplete block designs. It will be described why they are extremely useful for the design of statistical experiments, especially in biology and medicine.

Period	19 Jul 2018
Event title	Algebra and its applications
Event type	Conference
Location	EstoniaShow on map